Time-Constrained Temporal Logic Control of Multi-Affine Systems

In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically co-safe linear temporal logic formulas over rectangular regions in the state space. The proposed algorithm is based on the estimation of time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition system and an automaton that enforces the satisfaction of the specification. A random optimization algorithm is used to iteratively improve the solution

Conforming restricted Delaunay mesh generation for piecewise smooth complexes

A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted, conforming restricted Delaunay representation for domains specified as a (non-manifold) collection of piecewise smooth surface patches and curve segments, (ii) a protection strategy for domains containing curve segments that subtend sharply acute angles, and (iii) a new class of off-centre refinement rules designed to achieve high-quality point-placement along embedded curve features. Experimental comparisons show that the new Frontal-Delaunay algorithm outperforms a classical (statically weighted) restricted Delaunay-refinement technique for a number of three-dimensional benchmark problems.Comment: To appear at the 25th International Meshing Roundtabl

Proofreading tile sets: Error correction for algorithmic self-assembly

For robust molecular implementation of tile-based algorithmic self-assembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (ε) can be reduced to an arbitrarily low rate - but at the cost of reduced speed (r) for the self-assembly process. For tile sets directly implementing blocked cellular automata, it was shown that r ≈ βε^2 was optimal. Here, we show that an improved construction, which we refer to as proofreading tile sets, can in principle exploit the cooperativity of tile assembly reactions to dramatically improve the scaling behavior to r ≈ βε and better. This suggests that existing DNA-based molecular tile approaches may be improved to produce macroscopic algorithmic crystals with few errors. Generalizations and limitations of the proofreading tile set construction are discussed

Facet-sparing lumbar decompression with a minimally invasive flexible MicroBlade Shaver® versus traditional decompression: quantitative radiographic assessment.

BackgroundLaminectomy/laminotomy and foraminotomy are well established surgical techniques for treatment of symptomatic lumbar spinal stenosis. However, these procedures have significant limitations, including limited access to lateral and foraminal compression and postoperative instability. The purpose of this cadaver study was to compare bone, ligament, and soft tissue morphology following lumbar decompression using a minimally invasive MicroBlade Shaver® instrument versus hemilaminotomy with foraminotomy (HL).MethodsThe iO-Flex® system utilizes a flexible over-the-wire MicroBlade Shaver instrument designed for facet-sparing, minimally invasive "inside-out" decompression of the lumbar spine. Unilateral decompression was performed at 36 levels in nine human cadaver specimens, six with age-appropriate degenerative changes and three with radiographically confirmed multilevel stenosis. The iO-Flex system was utilized on alternating sides from L2/3 to L5/S1, and HL was performed on the opposite side at each level by the same investigator. Spinal canal, facet joint, lateral recess, and foraminal morphology were assessed using computed tomography.ResultsSimilar increases in soft tissue canal area and decreases in ligamentum flavum area were noted in nondiseased specimens, although HL required removal of 83% more laminar area (P < 0.01) and 95% more bone resection, including the pars interarticularis and facet joints (P < 0.001), compared with the iO-Flex system. Similar increases in lateral recess diameter were noted in nondiseased specimens using each procedure. In stenotic specimens, the increase in lateral recess diameter was significantly (P = 0.02) greater following use of the iO-Flex system (43%) versus HL (7%). The iO-Flex system resulted in greater facet joint preservation in nondiseased and stenotic specimens. In stenotic specimens, the iO-Flex system resulted in a significantly greater increase in foraminal width compared with HL (24% versus 4%, P = 0.01), with facet joint preservation.ConclusionThe iO-Flex system resulted in significantly better decompression of the lateral recess and foraminal areas compared with HL, while preserving posterior spinal elements, including the facet joint

Facets for Art Gallery Problems

The Art Gallery Problem (AGP) asks for placing a minimum number of stationary guards in a polygonal region P, such that all points in P are guarded. The problem is known to be NP-hard, and its inherent continuous structure (with both the set of points that need to be guarded and the set of points that can be used for guarding being uncountably infinite) makes it difficult to apply a straightforward formulation as an Integer Linear Program. We use an iterative primal-dual relaxation approach for solving AGP instances to optimality. At each stage, a pair of LP relaxations for a finite candidate subset of primal covering and dual packing constraints and variables is considered; these correspond to possible guard positions and points that are to be guarded. Particularly useful are cutting planes for eliminating fractional solutions. We identify two classes of facets, based on Edge Cover and Set Cover (SC) inequalities. Solving the separation problem for the latter is NP-complete, but exploiting the underlying geometric structure, we show that large subclasses of fractional SC solutions cannot occur for the AGP. This allows us to separate the relevant subset of facets in polynomial time. We also characterize all facets for finite AGP relaxations with coefficients in {0, 1, 2}. Finally, we demonstrate the practical usefulness of our approach. Our cutting plane technique yields a significant improvement in terms of speed and solution quality due to considerably reduced integrality gaps as compared to the approach by Kr\"oller et al.Comment: 29 pages, 18 figures, 1 tabl

Influence of the Fermionic Exchange Symmetry beyond Pauli's Exclusion Principle

Pauli's exclusion principle has a strong impact on the properties of most fermionic quantum systems. Remarkably, the fermionic exchange symmetry implies further constraints on the one-particle picture. By exploiting those generalized Pauli constraints we derive a measure which quantifies the influence of the exchange symmetry beyond Pauli's exclusion principle. It is based on a geometric hierarchy induced by the exclusion principle constraints. We provide a proof of principle by applying our measure to a simple model. In that way, we conclusively confirm the physical relevance of the generalized Pauli constraints and show that the fermionic exchange symmetry can have an influence on the one-particle picture beyond Pauli's exclusion principle. Our findings provide a new perspective on fermionic multipartite correlation since our measure allows one to distinguish between static and dynamic correlations.Comment: title has been changed; very close to published versio